75.14.20 problem 346

Internal problem ID [16934]
Book : A book of problems in ordinary differential equations. M.L. KRASNOV, A.L. KISELYOV, G.I. MARKARENKO. MIR, MOSCOW. 1983
Section : Chapter 2 (Higher order ODEs). Section 14. Differential equations admitting of depression of their order. Exercises page 107
Problem number : 346
Date solved : Tuesday, January 28, 2025 at 09:42:40 AM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} y^{\prime \prime }&=y^{\prime } \ln \left (y^{\prime }\right ) \end{align*}

With initial conditions

\begin{align*} y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=1 \end{align*}

✓ Solution by Maple

Time used: 0.187 (sec). Leaf size: 21

dsolve([diff(y(x),x$2)=diff(y(x),x)*ln(diff(y(x),x)),y(0) = 0, D(y)(0) = 1],y(x), singsol=all)
 

\[ y = -\operatorname {Ei}_{1}\left (-2 i {\mathrm e}^{x} \pi \_Z463 \right )+\operatorname {Ei}_{1}\left (-2 i \pi \_Z463 \right ) \]

✗ Solution by Mathematica

Time used: 0.000 (sec). Leaf size: 0

DSolve[{D[y[x],{x,2}]==D[y[x],x]*Log[D[y[x],x]],{y[0]==0,Derivative[1][y][0] ==1}},y[x],x,IncludeSingularSolutions -> True]
 

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